A new family of exponential iteration methods with quadratic convergence of both diameters and points for enclosing zeros of nonlinear equations

This paper presents a new class of exponential iteration methods with global convergence for finding a simple root x∗x∗ of a nonlinear equation f(x)=0f(x)=0 in the interval [a,b][a,b]. The new methods are shown to be quadratically convergent. Both the sequences of diameters {bn−an}{bn−an} and the iterative sequence {xn−x∗}{xn−x∗} are quadratically convergent to zero. The theoretical analysis and numerical experiments show that new exponential iterative formulae are effective and comparable to those of the well-known Newton and Steffensen methods.